Process control systems, such as distributed or scalable process control systems, can be utilized in chemical, petroleum and other industrial processes. A typical process control system includes one or more process controllers communicatively coupled to each other, to at least one host or operator workstation and to one or more field devices via analog, digital or combined analog/digital buses.
A common approach to advanced industrial process control involves the use of MPC (Model-based Predictive Control) techniques. MPC is a control strategy that utilizes an optimizer to solve for a control trajectory over a future time horizon based on a dynamic model of the process. MPC technology utilizes a mathematical model representation of the process. The models are then utilized to predict the behavior of dependent variables (e.g., controlled variables, CVs) of a dynamic system with respect to variations in process independent variables (e.g., manipulated variables, MVs). In a typical implementation, the MPC computes a future sequence of manipulated variables that optimize certain performance-related criterion involving future process trajectories, with respect to various constraints. From the optimal sequence of future manipulated variables, only the first manipulated variable is actually applied to the process. Then, measured process variables can be utilized to update the internal process model and the process is repeated.
A number of MPC approaches have been implemented and discussed in MPC-related literature. For example, the article entitled “Constrained model predictive control: Stability and optimality” by D. Q. Mayne, et al., Automatica 36 (2000), pp. 789-814, provides a good survey of MPC approaches and principals, and is incorporated herein by reference in its entirety. Another article, which is incorporated herein by reference, describes MPC principals and technique and is entitled “A survey of industrial model predictive control technology” by S. Joe Qin, et al., Control Engineering Practice 11 (2003), pp. 733-764.
In general, controlled processes are typically nonlinear in nature, (i.e., they cannot be accurately described by the mathematical model with linear relations among the inputs, the states and the outputs). The majority of industrial MPC techniques utilize linear models that are not sufficiently accurate because of process nonlinearities. Hence, if an operating point in the process changes, the controller may perform poorly. There are approaches for adapting the internal model to changing operating condition by some kind of interpolation among models corresponding to different (steady-state) operating points (e.g., gain scheduling). These approaches are non-optimal during the transition between the operating points unless the transition is very slow.
KF (Kalman Filtering) is an optimal filtering technique commonly utilized for estimating the state variables of a linear system. Kalman filtering is a time domain operation that is suitable for use in estimating the state variables of linear time-varying systems that can be described by a set of linear differential equations with time-varying coefficients. Kalman filtering approaches have found applications in state estimation in many systems that may be approximately described as linear. Moreover, they can be utilized for estimating unknown inputs of specific classes by augmenting the process model by an appropriate input generator. The basic Kalman filter technique cannot accommodate general nonlinear systems. The Kalman filter can be utilized to estimate states in nonlinear systems based on quasi-linearization techniques.
Such techniques, among which is that referred to as EKF (extended Kalman filter), when restricted to computationally feasible methods, result in sub-optimal estimators, which do not yield minimal error estimation. However, applications of these suboptimal filters often yield satisfactory results in the industrial practice. KFs (EKFs) are used in conjunction with MPC when the latter uses the state-space representation of the process model and process state is not directly measurable. Then, MPC uses the state estimate of KF (EKF) to predict future process behavior. Moreover KF (EKF) may be used for estimating unmeasured inputs (disturbance variables, DVs) of specific forms to further improve predictions of process behavior resulting in an enhanced control performance.
The majority of prior art MPC approaches with a linear internal model utilize the formulation of the optimization problem leading to Quadratic Programming (QP) (i.e., optimization of quadratic cost function subject to linear constraints). There exist fast and reliable QP solvers that fully satisfy the requirements for application in real-time control. Utilizing the non-linear internal model results in a general nonlinear programming problem; algorithms for solving these general problems require more computational effort and are less reliable compared to those used for QP. Some of prior art nonlinear MPC approaches utilize linear approximation (linearization) of the internal model around a nominal trajectory. The time-varying linear system arising from this linearization describes deviations of the process trajectory from the nominal one. This approximation is accurate if the deviations are small. The optimization technique under discussion optimizes the deviation trajectories, using the QP problem, The optimal deviations are utilized for updating the nominal trajectory and the process (linearization, QP) is repeated in an iterative process, known as SQP (Sequential Quadratic Programming).
Based on the foregoing it is believed that a need exists for a predictive controller, which is capable of handling a broad class of non-linear processes without extensive computational effort associated with solving a general non-linear program. A possible way to achieve this goal is to obtain a nominal process trajectory that is reasonably close to the optimal one, thus eliminating the necessity of iterative process including QP as in the SQP technique. Hence, it is also believed that a need exists for a nominal (target) trajectory generator for predictive control of nonlinear processes. Utilizing an extended Kalman filter for estimating this future nominal trajectory is particularly appealing, because this filter is, in many cases, already used for estimating unknown process states.